Nonparametric Estimation of the Hazard Ratio

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Abstract
A nonparametric estimate of the hazard ratio function is developed and applied to the time-dependent survival advantage of having achieved an objective response to treatment for a given disease. The method computes the total exposure to risk of failure, or dying, among patients in either of two disease states (nonresponder/responder). By assuming constant hazard rates between observed failure times, and using smoothing techniques of exploratory data analysis, the log hazard ratio function is computed and plotted versus time. The method is applicable to any binary, time-dependent covariate, of which disease state is a particular example. Continuous-valued covariates may be handled by a plot of updated covariate percentiles for failures. The methods are applied to data on leukemia patients and to a simulated example and compared with standard Cox regression results.

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